On the other hand, since \((d,e) \in G(M) \cap G(Q)\) , \(e = Qd\)  and \(e \in Md\) .
From (REF ), \(d = T(Qd) = Te\) , and so \(e \in M(Te) = (MT)e\) . Thus \(e\)  is, in fact, a fixed point of \(MT\) .

The final result of this section, Corollary REF , is a restatement of [1]} which, in turn, generalizes [2]}. We will use Fact REF  below, see[3]} and [3]} for proofs.
